Crown lawyers on behalf of the US Government sought a judicial review of that decision on the grounds the District Court could not make a ruling under the Extradition Act.
The lawyers for the US Government argued Dotcom and his associates have access to some documents, including emails and their bank account records.
They said that under US law, disclosure is only granted once the accused appears in a US court.
Lawyers on behalf of the US Government also said they would not be able to disclose all the information in the 21-day period required.
They told the court there were over 10 million emails seized and "voluminous'' financial records.
FBI agent Michael Postin said in an affidavit that the items seized in New Zealand alone are estimated to contain more that 150 terabytes of data.
To give an idea of how much work was involved, he said it had taken 10 days to copy 29 terabytes.
Mr Postin said copying all of the data could take two and a half months. He said some of it could not be copied because it has been encrypted.
However, Justice Winkelmann ordered that the authorities begin making copies of all the information.
She said that the US Government had "ample means'' to do the work. '' ... [T]he expense involved in copying must be dwarfed by the other costs of an investigative and prosecutorial operation of this size.''
The judge went on to say that if Dotcom is extradited to the US then the work will not have been a waste of time.
But she said it was not possible to determine yet whether or not the US Government had an obligation to release the information to Dotcom's lawyers.
Justice Winkelmann ordered that a further two-day hearing be held to determine that matter.
Dotcom and associates Finn Batato, Mathias Ortmann and Bram van der Kolk face an extradition hearing in August which will determine whether or not they are to fly to the US to face charges including copyright infringement and wire fraud relating to the file-sharing website Megaupload.
Prosecutors allege a "mega conspiracy''; Dotcom denies the charges and says his website was legitimate.
Dotcom request to drop charges a waste of time - US Attorney's office
Meanwhile the the US Attorney's office has rubbished Kim Dotcom's plea to have criminal charges dropped, saying the request is a waste of court time and resources.
The Auckland-based Megaupload founder claimed earlier this month that America had no jurisdiction over his Hong Kong-based cloud-storage service.
But according to court papers filed by Neil MacBride, US Attorney for Eastern District of Virginia, and reported in CNET News, Dotcom's request to dismiss criminal copyright charges should be denied.
In a 20-page document, lawyers for the American government also argued that Dotcom's request to dismiss the charges was "premature" because none of the defendants have refused to appear before the court.
Yesterday a former New York federal judge Abraham David Sofaer joined the Dotcom drama.
He claimed it was "outrageous" that the US government was refusing to return 66.6 million files of data to Megaupload users.
The ex judge told wired.com: "I was thinking the government hadn't learned to be discreet in its conduct in the digital world. This is a perfect example on how they are failing to apply traditional standards in the new context."
